Good neighbors are hard to find: computational complexity of network formation

• Published in: Review of economic design Vol. 12; no. 1; pp. 1 - 19
• Main Authors: Baron, Richard, Durieu, Jacques, Haller, Hans, Savani, Rahul, Solal, Philippe
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01-04-2008; Springer Nature B.V; Springer Verlag
• Subjects: Algorithms; Behavioral/Experimental Economics; Computer science; Costs; Decision analysis; Economic theory; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Economics and Finance; Equilibrium; Game Theory; Humanities and Social Sciences; Investigations; Lead Article; Microeconomics; Social and Behav. Sciences; Studies; D85; Network formation; Computational complexity; Strategic games; D02; C72; Strategic games · Network formation · Computational complexity
• ISSN: 1434-4742; 1434-4750
• DOI: 10.1007/s10058-008-0043-x

We investigate the computational complexity of several decision problems in a simple strategic game of network formation. We find that deciding if a player has a strategy that guarantees him a certain payoff against a given strategy profile of the other players is an
NP
-complete problem. Deciding if there exists a strategy profile that guarantees a certain aggregate payoff is also
NP
-complete. Deciding if there is a Nash equilibrium in pure strategies which guarantees a certain payoff to each player is
NP
-hard. The problem of deciding if a given strategy profile is a Nash equilibrium is investigated as well.